{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _Modeling of Scalar Quantum Chain_\n",
    "\n",
    "<img src=\"images/line_circs_site.png\" alt=\"Scalar Chain\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Contributor\n",
    "Alexander Yu. Vlasov\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model of discrete quantum walk on a chain. Only standard Python packages are used here. Qiskit is considered in [other notebooks](qubit_chain_mod.ipynb) explaining modeling of [qubit chain](qubit_chain.ipynb). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "from scipy import linalg\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# swap is 2x2 matrix\n",
    "swap = np.array([[0, 1], [1, 0]], dtype=complex)\n",
    "\n",
    "# Hadamard coin\n",
    "c_Hadamard = (1/math.sqrt(2))*np.array([[1, 1], [1, -1]], dtype=complex)\n",
    "\n",
    "# Balanced coin (not used)\n",
    "c_bal = (1/math.sqrt(2))*np.array([[1, 1j], [1j, 1]], dtype=complex)\n",
    "\n",
    "# step with swap and coin\n",
    "s_coin = c_Hadamard.dot(swap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Number of nodes (should be odd)\n",
    "n_nodes = 15\n",
    "\n",
    "# Step 1 includes swap and coin for first partition\n",
    "Step1 = np.identity(n_nodes, dtype=complex)\n",
    "for i in range(0,n_nodes-1,2):\n",
    "    for i1 in range(0,2):\n",
    "        for i2 in range(0,2):\n",
    "            Step1[i+i1,i+i2] = s_coin[i1,i2]\n",
    "\n",
    "# Step 2 includes swap for second partition\n",
    "Step2 = np.identity(n_nodes, dtype=complex)\n",
    "for i in range(1,n_nodes,2):\n",
    "    for i1 in range(0,2):\n",
    "        for i2 in range(0,2):\n",
    "            Step2[i+i1,i+i2] = swap[i1,i2]            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Vector with chain nodes\n",
    "ch = np.zeros(n_nodes, dtype=complex)\n",
    "\n",
    "# Initial distribution for symmetric walk with Hadamard coin\n",
    "# two central nodes\n",
    "n_pos = n_nodes//2\n",
    "ch[n_pos] = 1/math.sqrt(2)\n",
    "ch[n_pos+1] = 1j/math.sqrt(2)\n",
    "\n",
    "# Alternative initial distribution also could be used\n",
    "#ch[0] = 1\n",
    "\n",
    "# Probability from complex amplitude\n",
    "def abs2(x):\n",
    "    return x.real**2 + x.imag**2\n",
    "\n",
    "# Vector with probabilities\n",
    "ch2 = np.zeros(n_nodes, dtype = float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.  0.  0.  0.  0.  0.  0.  0.5 0.5 0.  0.  0.  0.  0.  0. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xca8e370630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.   0.   0.   0.   0.   0.   0.25 0.25 0.25 0.25 0.   0.   0.   0.\n",
      " 0.  ]\n",
      "[0.   0.   0.   0.   0.   0.25 0.   0.25 0.25 0.   0.25 0.   0.   0.\n",
      " 0.  ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcaa147d898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.    0.    0.    0.    0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125\n",
      " 0.    0.    0.   ]\n",
      "[0.    0.    0.    0.125 0.    0.125 0.125 0.125 0.125 0.125 0.125 0.\n",
      " 0.125 0.    0.   ]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcaa147d908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.     0.     0.0625 0.0625 0.0625 0.0625 0.25   0.     0.     0.25\n",
      " 0.0625 0.0625 0.0625 0.0625 0.    ]\n",
      "[0.     0.0625 0.     0.0625 0.0625 0.25   0.0625 0.     0.     0.0625\n",
      " 0.25   0.0625 0.0625 0.     0.0625]\n"
     ]
    },
    {
     "data": {
      "image/png": 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phUHnxPvsT/qtDbU01AZJ9Kdte09lD036ylZWuaad88OQS0g9g6OMZ6ZsfV+Vu1ayoi5IS7jGtvfMnZ3perl+pElf2cqad7dz1Gi9nzHQpSNH21nr4orYc+HdYjVeU/5SUtIXkTtF5H0ROS4i35zh+Y+LyBsikhGRLxY9NyUiR/L/9tkVuPKneDJFQ22QSIN9o0bQ9XKd1FnmurizibWE6BlMM5HRm+r8ZN6kLyJVwKPA54AtwFdEZEvRZl3Aw8BTM7zFqDHmhvy/u8qMV/mctS6u3aPGqCZ9R4xNTtE7NGpLn6RisdYwWQNdA3p25ieljPS3AceNMZ3GmAngaeDuwg2MMQljzFuAHtKXuVy5pv0JZGV9NS3hGr2Ya7OugTTGXFjQ3E56f4U/lZL01wPdBb/35B8rVZ2IHBaRgyJyz0wbiMjX89sc7uvrW8BbKz8Zz0xxcnDUkakCyI32tZ+LvaYbrTkx0s//Hei8vr+UkvRnOk9fyL3V7caYrcBXgb8RkcsveTNjHjPGbDXGbG1tbV3AWys/6R5IkzXlr4s7Gy3btJ+d3TWLrQrV0BSq1goenykl6fcAbQW/bwB6S/0AY0xv/r+dwK+BGxcQn6ogcavRmo03ZhWKRcKcOT9OajzjyPsvR4lkipZwDSvrqx15/1gkrCN9nykl6R8CrhCRmIjUAPcBJVXhiEiTiNTmf44AO4B3Fhus8re4zS2Vi01PF+ho3zadNjdaKxaNhHVO32fmTfrGmAzwDeBF4F3gGWPMMRH5jojcBSAit4hID3Av8F0ROZZ/+UeAwyJyFPgV8JfGGE36S1Q8maI5XMPKkDOjRr0waL9EMuXI1I5lUyTM6fNjpCf07MwvgqVsZIx5AXih6LFvF/x8iNy0T/HrDgDXlRmjqhDxZIpoizPz+XBhGT6dLrDHyHiGs8Pjjo/0IbfGwpZ1jY59jiqd3pGrbJPrye7MfD5AqCbI2sY6vTBoE6funi6kN9X5jyZ9ZYvUeIYz58cdqfcupBcG7RN3IelbU3J6HcY/NOkrW1g7tRP13oVirXph0C5O1uhbwrVB1jTW6v0VPqJJX9liel1cB0eNkKsMGkxPci494ejnLAeJZIrLVtZRX1Pl6Ofo/RX+oklf2SI+3VLZuQu5oHPEdnK6XNMS07JNX9Gkr2wRT6ZZ21hHqKakgrBF08Zr9kn0O1uuaYlFwgykJhhKTzr+WWp+mvSVLexeF3c27c0hAqJlm+UaTE1wLj1p+wpnM5m+v0KneHxBk76yRaLf3nVxZ1MTDLChSVdkKlfcpQvvcKGDpx6o/UGTvirbufQEA6kJxxqtFdMLg+WbXhfX4RJbgLb82ZkeqP1Bk74q24V6b+dH+rnPCRPvS2HMQpq9qkKJ/hQBgbYm5w/UtcEq1jfV63UYn9Ckr8pmjbrdHOmnJqboGxl35fOWos5kirbmEDVBd1JAtEVvqvMLTfqqbPG+/Kix2Z2kP13Bozf8LFoimXJlPt+yKV+2qWdn3tOkr8oW70+zoSlEbdDZm3wsm7TFclmMMfk+Se4l/VgkzMh4huSI3lTnNU36qmxOrYs7m3Wr6qmpCuiFwUU6OzxOemLK1aSv91f4hyZ9VRZjDIlk2pV6b0tVQGhvCekc8SK50Wit2Kb8RX79zrynSV+VpW9knJHxjKN99Geit/YvnhdJf92qOqqrRM/OfECTvirLdKO1VnfKNS25Wv002axeGFyoRDJFTVWAdavqXfvMYFWA9mY9O/MDTfqqLE6vizubWCTMRCZL79Coq5+7FHQmU2xsCVEVEFc/V8/O/EGTvipLPJmmukpY3+TeqBF0vdxyOL0u7mysO6n17MxbmvRVWeLJEdqb3R81aj+XxZnKGk70u3vh3RKNhBnPZDl1fsz1z1YXaNJXZUkk3Wm0Vmz1ilpCNVV6YXCBes+NMjGV9WykD3qg9pomfbVo2awh3p9yrf1CIRHRW/sXwYvKHYv1mXqg9pYmfbVovUOjTGSynoz0QS8MLsaFPknuJ/01K+qor67S9hke06SvFs2tdXFnE4uE6R4cZXIq68nnV6LOvhShmipWr6h1/bMDASGqbbE9p0lfLdp0uaZHST8aCTOVNXQPpD35/EqU6M81WhNx98K7JRYJ6dmZxzTpq0WLJ9PUV1exptH9USMUXBjUkWPJ4smUKwunzCYWCdM9kNazMw9p0leLZjVa827UmL8wqHPEJZnIZOkeSLt+I12haEuYTNbQM6g31XlFk75atIRH9d6WplA1K+urdaRfou7BNFnj3XQc6P0VfqBJXy3K5FSWroE0UQ/KNS0iohU8C+Dmurizse6k1rJN72jSV4vSMzjKVNZ4Vq5piUXC01VEam7T5ZoeTu80h2torAvqSN9DJSV9EblTRN4XkeMi8s0Znv+4iLwhIhkR+WLRcw+JyIf5fw/ZFbjy1oXKHe9G+rnPD3Py3Chjk1OexlEJOpMpVoWqaQrXeBaDnp15b96kLyJVwKPA54AtwFdEZEvRZl3Aw8BTRa9tBv4cuBXYBvy5iDSVH7byWny6Rt/bkX5UK3hK5va6uLPRpO+tUkb624DjxphOY8wE8DRwd+EGxpiEMeYtoLgO67PAL4wxA8aYQeAXwJ02xK08Fk+O0FgXpClU7Wkcm7SfS8niyZSnF94t0UiY3iE9O/NKKUl/PdBd8HtP/rFSlPNa5WO5eu8Gz8o1LVHt51KS0YkpTg2NedJorVgsEsYYONGv12K8UErSn2mvLrUhdkmvFZGvi8hhETnc19dX4lsrL7m9Lu5sGmqDtK6o1ZH+PLzsuVPMWi9Xp3i8UUrS7wHaCn7fAPSW+P4lvdYY85gxZqsxZmtra2uJb628MjY5xclzo76YH4ZcNYomkLklPOyuWcwq89XvzBulJP1DwBUiEhORGuA+YF+J7/8i8BkRacpfwP1M/jFVwazTci/rvQvlLgzqVMFcrOkvP0zvrKirJtKgZ2demTfpG2MywDfIJet3gWeMMcdE5DsicheAiNwiIj3AvcB3ReRY/rUDwF+QO3AcAr6Tf0xVMK/WxZ1NNBImOTLO8Nik16H4VjyZonVFLQ21Qa9DAbTxmpdK+gswxrwAvFD02LcLfj5EbupmptfuBfaWEaPyGWtU7eXduIUurMiU5roNKz2Oxp8SyZQvpnYssUiYX72v1++8oHfkqgWLJ0eINNSyos7bck3LhRWZRjyOxL/iyZRvzswgd3bWN6xnZ17QpK8WzC+VO5aNLSFE0HYMsxganaQ/NeGbazBw4f4KLdt0nyZ9tWCdyZRvpnYA6qqrWLeyfvpag7qYdcHUL9VWoPdXeEmTvlqQ4bFJkiPjnrdfKBaLhInrqHFGVo3+Jh+N9K0DkFbwuE+TvlqQC+vi+mekD/mk3zeCMaXeN7h8dPalEIH2Zv98Z7mzszqt4PGAJn21IJ3T3TX9NdKPRsKcH8swmNYLg8US/SnWraynrrrK61AuEmsN6/SOBzTpqwVJJNOI5C6e+ol1YVDn9S8VT6Z8NbVj0bMzb2jSVwsST474ctQ4fWFQ18u9iDGGuE9aKheLtujZmRc06asFifenfXWTj2VDUz3BgGhf/SL9qQmGxzK+/M6ssw+d13eXJn1VMmMM8b4RX5VrWqqrArQ16639xeI+arRWzDr70O/MXZr0VckG05OcH8v47iKuRRuvXcrPSb+tOURVQLRs02Wa9FXJ/LIu7myiLWESyZReGCwQT6YIBoQNTfVeh3KJ6qoAbU31OtJ3mSZ9VTK/rIs7m1hrmNHJKc6cH/c6FN9IJFO0N4cIVvlzV9f1ct3nz78E5Uvx5AhVPh01woVWz9p47YJ4MuWLHvqziUbCJPr17MxNmvRVyRLJNO3NIar9OmpsvdBiWUE2a0j0+6ulcrFNkTDpiSnODuvZmVv8ufcqX+pMpoj67KasQpc11lEbDOgNWnmnz48xNpn1/Ugf9P4KN2nSVyUxxuQX4vDnfD5AICBEW7SCx2JVxfipDXaxWETLNt2mSV+V5Mz5cUYnp3zVk30muQuDOtKHC22L/Ty9s25lPTXBgN5U5yJN+qoknT5bF3c20UiYroE0U1m9MJhIpqgNBljbWOd1KLPKnZ2FdHrHRZr0VUmmWyr7fKS/KRJmcspwcnDU61A8F8+vixsIiNehzCmWr+BR7tCkr0oST45QGwxwmY9HjVC4IpNO8cT7/dlorVg0EqarX8/O3KJJX5UknkwTbamMUSPoikyZqSxd/Wnfn5lB7uxsYipL7zk9O3ODJn1VknjSn43WikUaamioDS77apCewVEyWeP7azBwofGaLqjijqDXAfid1Y98U6t/SxUL9Z4b5YTNa8UaDN0Do3x6y1pb39cJIqLr5ZKb2gH/X4OBCzH+8wd91Nh8419NMMBN7asQ8fcZKsBbPedYVV9Du8P3wmjSn8dTr3XxrZ+8zXN/vJ2bNzZ5Hc6cxjNT3PPofsfubrx67QpH3tdum1c38PIHfYxnpqgN+muxF7e8eWIQ8HeNvqW1oZaWcA17OuLs6Yjb/v7/5d7r+aObN9j+vnYyxvC//f3bjE5M8fN//XFHD1Ka9OeQzRr+9je5P8I9HZ3cvPFmjyOa274jvZwdHucv7rmWzTafmdQEhes3rLL1PZ3yBzeu5ydvnuQfj57y/c7uhPHMFE+91sUnr2qlpaHW63DmJSL8/Z/soMeBiqtv/8Pb/G1HnD+8ab2vR/uvnxjkrZ4h/uKeax2PU5P+HH79wVniyRRXr13BP719mp7BNBua/DmvbYxh7/4EV61ZwQO3tvv6D9xpH7siwhWrG9hTATu7E/Yd6SU5MsHunZu8DqVkbc0h2prt37d274zxzed/y8HOAW6/vMX297fLno44K+ur+aOb1jv+WXohdw57OuKsbazjvz+4FRHhyQMJr0Oa1Sud/bx76jy7dkaXXZIrJiLs2hnjnVPneTU+4HU4rio8+O/Y7N8k55Z7blxPc37qyK+6B9K8eOw0X721nVCN8+NwTfqzePfUefYf7+fB7Rtpaw7x+esu4+nXuhkZz3gd2oz2dsRpDtdw9w3OjxQqwR/cuJ6mULWvd3Yn6MH/YnXVVdx/azsvvXfGt2W8Tx5IEBDhwds3uvJ5mvRn8fj+OPXVVXx1WzuQO00cHs/w7OFujyO7VDyZ4qX3zvLAre3UVS/PC5fFcjv7Rv7Hu/7d2Z2gB/9Lfe22jQQDwhM+PFMfGc/wo0PdfP66y7hspTvrVGjSn0FyZJy/P9LLH928nlWhGgBuaFvFTe2rePxAwnd3Dj6xP04wIDxwmzsjhUrx4O3+3dmdoAf/ma1urOMLH13HM4e7GRqd9Dqci/z4cDfD4xl27Yy59pklJX0RuVNE3heR4yLyzRmerxWRH+Wff1VEovnHoyIyKiJH8v/+m73hO+MHB7uYyGR5ZMfFX8TunZs40Z/ml++d9SiySw2NTvLj13v4wvXrWO3zFglus3b2Hx/u5vyYv3Z2J0wf/F2aJqgku3bGSE9M8cwh/5ypT2UNj+9PcPPGJm5oc68ybt6kLyJVwKPA54AtwFdEZEvRZruBQWPMZuCvgf9Y8NzvjDE35P/9S5vidsx4Zoq/O3iCT17VyuVFZY+fvWYN61fVs6ej06PoLvWjQ12kJ6bYtcO9kUIl2bUzRmpiih+95p+d3QkXHfxX6MG/2LXrV3JrrJknDiTITGW9DgeAl949Q9dAmt0ujvKhtJH+NuC4MabTGDMBPA3cXbTN3cCT+Z+fBe6QCr2KlCt3G5/xdCtYFeCh7Rs52DnAsd4hD6K7WGYqy5MHTnBrrJlr16/0Ohxfunb9Srb5bGd3gh7857drZ4yT50Z58dgZr0MBctWB61fV85kta1z93FKS/nqgcJjUk39sxm2MMRlgCLDqxWIi8qaIvCwiH5vpA0Tk6yJyWEQO9/X1Leh/gJ0Ky912bo7MuM2Xb2knVFPF3o6Eu8HN4MVjZzh5btT1kUKl2Z3f2X/+jj92drvpwb80n/rIGtqbQ+zd731F19snh3g1PsDD26MEXV5zupRPm2nEXnwlc7ZtTgHtxpgbgT8FnhKRxks2NOYxY8xWY8zW1tbWEkJyRinlbivrq7n35g389GgvZ4fHXI7wYns6OtnYEuKOj7h/iquJAAAS4ElEQVQ7Uqg00zv7Ei3f1IN/aaoCwiM7orx+YpAj3ec8jWXv/jjhmiq+vK3N9c8uJen3AIWRbQB6Z9tGRILASmDAGDNujOkHMMa8DvwOuLLcoJ1SarnbIztiTGazfP+VEy5Fdqk3uwZ5o+scD2+PUuXzdsdeqwoID2+PcvjEIEc93tmdoAf/0t27tY0VtUFP7984e36Mnx7t5d6tbTTWVbv++aUk/UPAFSISE5Ea4D5gX9E2+4CH8j9/EfilMcaISGv+QjAisgm4AvDPVdACCyl3i0bC3HH1Gr7/ahdjk1MuRXixvfsTrKgNcu9W90cKlehLt3i/sztBD/4L01Ab5Mu3tPHCb09xasib/v1/d/AEmazh4e1RTz5/3qSfn6P/BvAi8C7wjDHmmIh8R0Tuym+2B2gRkePkpnGsss6PA2+JyFFyF3j/pTHGl/fFL7TcbdfOKAOpCf7hyEmHI7tU77lRXvjtKb58SxsNtdo+qRQNtUG+5PHO7gQ9+C/cQ9ujGGN48oD7Z+pjk1P84NUu7rh6zfQqb24r6QqCMeYFY8yVxpjLjTH/R/6xbxtj9uV/HjPG3GuM2WyM2WaM6cw//pwx5hpjzPXGmJuMMT917n/K4i2m3O32TS185LJG9nYkMMbdm7W+98oJjDE85NFIoVI9vD1K1hi+5+G0nJ304L84bc0hPnvNWn74WhfpCXfbqvz9mycZSE14ev1F78jlQrnbQr4IEWHXjijvnxlm//F+B6O7WHoiww9f6+LOa9c60pVwKWtrDvGZLWt56lX3d3Yn6MF/8XbvjDE0Oslzb7h3pp6rDoyz5bJGbtvU7NrnFlv2Sd8qd7ttUzPXrFtYudtdN6wj0lDr6s1az73ew9DopNZjL9Luj+V29udd3NmdoAf/8ty8sYmPbljJ4x1xsi61Vek4nuSDMyPs2hnztBnesk/6VrnbYpJobbCKr922kV+938fv+kYciO5i2fxt29dvWOn7Vbz8amt+Z9+7372d3QnPvXFSD/5lEBF274zRmUzx8gfu3Bu0pyNOpKGWL1x/mSufN5tln/TLLXe7/7Z2aoIBHnfhho9ff3CWzmTK85FCJctNy8Xo7Evx8ofe3QhYjmzW8HhHXA/+Zfr8dZexprHWlYqu42dH+PX7fTx4+0bPl/Bc1knfjnK3SEMt99ywjudeP8m59ITNEV7MWtTl89d5O1KodNbOXqk3a+nB3x7VVQEevD1Kx/Ek750+7+hnPb4/Tk0wwFdvbXf0c0qxrJO+XeVuu3bGGJ2c4ocONvV67/SFRV2qXb5te6mpCeZ29t98mOT908Neh7NgezsSevC3yVe3tVNXHeBxB9uqnEtP8NwbPfzBDeuJ+GDN4mWbPaxyt/u2lV/udvXaRnZsbuHJAwkmHWrqtbcjTl11YHpRF1We6Z3dB31YFuK90+fpOJ7Ug79NmsI1/OFNG/jJkZMkR8Yd+YynXutibDLLIzujjrz/Qi3bvxqr3O3B26O2vN/unTFOnx/jZ2+ftuX9Ck0v6nLThulFXVR5rJ39+TdP0u/Qzu6ExzsSevC32a4dMSYyWZ56tcv2956cyvK9AyfYuTnC1WsvaTvmiWWZ9J0od/vElavZFAmzpyNu+81asy3qosqza0eUiUyWHziwszshOTLOT46c1IO/zTavbuATV7XyvVdOMJ6xt63KC789xenzY75qhrcsk75V627nFxHId/A72n2ON7oGbXtfa1GXT1zVyubVDfO/QJVs8+oV/N6VrfzdQft3difowd85u3bESI6M89Ojp2x7T2MMezvibGoN83tXetc9uNiyS/qFte43tdtb7vaHN22gsS5oa6/9nx49RXJk3FcjhaVk984YfcPj/KONO7sT9ODvrI9dEeHKNQ3stfFM/Y2uQY72DPHIjhgBHzXDW3ZJ38lyt3BtkK/c2s7P3j5Fz2C67PczxrCnI86VaxpmXdRFledjV0S4YnUDe/fbPy1nJz34O8u6f+OdU+c52GlPT8g9HXFW1lfzRzfN3ardbcsu6Ttd6/7Q7bkFWJ48kCj7vaYXddmh9dhOERF27YxxrPc8r8Z92QB2eppAD/7OuufG9TSHa2y5Wat7IM0/vX2ar2xrJ1Tjr2Z4yyrpu1Hrvm5VPZ+7di1PH+pmZLy8pl57OxI0h2u450Z/jRSWmj+4cT1NoWrf9to/2DnAO3rwd1xddRX339rOS++dIZFMlfVe33slgYjw0PbSWrW7aVklfbdq3XfvjDE8luHZw4u/WSuRTPHSe2e4v4RFXVR5cjv7Rv7Hu2c40V/ezu6EPfkV3fTg77yv3baRYEB4oowz9ZHxDE+/1s3nr7uMy1bW2xecTZZN0nez1v3G9iZubF/F4wcSi27q9cSBBMGA8LXb/DdSWIoevD23sz++P+F1KBfRg7+7VjfW8YWPruOZw90MjU4u6j1+fLib4fGMb6+/LJukb5W77XLpi9i9M8aJ/jQvvXd2wa8dGp3kmcPduUVdGktb1EWVx9rZf3y4m/Nji9vZnaAHf/ft2hkjPTHFM4cWfqY+lTU8cSDBzRubuKFtlQPRlW9ZJH2r3O2TV7Vyeas75W53XrOWdSvrFtVr31rURdvmumvXzhipRe7sTpg++H9UD/5uunb9SrbFmnniQILMAtuqvPTuGU70p3297y6LpG+Vu7k1ygcIVgV4aHuUg50DHOsdKvl11qIut8aauXb9whZ1UeWxdvbH9y98Z3fCM4e6cwd/n04TLGW7d8Y4eW6Un79zZkGv27s/zvpV9Xz2msW1anfDkk/6Vq37VWtWuF7udt8t7YRqqhZ0s5a1qItf5wOXul07cjv7Lxa4s9stM5XliQMJPfh75FMfWUN7c2hBFV3Heoc42DnAw9ujBH3cDM+/kdlkutZ9Z9T1creVoWq+ePMGfnq0l7PDYyW9Zk9HJ+3Ni1/URZXn01sWvrM74efv5Fd004O/J6oCwsPbo7x+YpAj3edKes2ejjihmiq+dEt5rdqdtuSTvlXrfvcN3pS7PbIjxmQ2y/cPzt/Uy1rU5ZEdi1/URZXH2tkPnxjkaIk7uxP2dMRpbw7xKT34e+ZLt7SxojZY0mI7Z4fH+OnRXr60tY2V9dUuRLd4SzrpW+VuD3hY7haLhLnj6tX84OAJxibnbupl16Iuqjz3bt1AQ22QvR712j/SfY7XTwzqwd9jDbVBvnRLGy/89hSnhkbn3Pb7r5wgkzU8vD3qTnBlWNJJ3yp3e8DjcrddO2L0pybYd6R31m1ODeUWdfnyLeUv6qLKs6Kumi/f0sb/99YpTg+VNi1np70dcT34+8TD26NkjeF7r5yYdZuxySm+/2oXd1y9hmgk7GJ0i7Nkk76fat1vv7yFq9eumLOp15MHcou6PFQBI4XlwNrZn3wl4ern6sHfX9qaQ3z2mrU89WoX6YmZ26r8w5GTDKQmKqb4YskmfT/VultNvd47Pcz+4/2XPG8t6vLZa+xb1EWVp605xGe25Hb20Qn3eu1/75UTZPXg7yu7dsYYGp3kuTdOXvKcVR34kcsauW1TswfRLdySTPp+rHW/6/p1RBpqZpwnfu6Nk7Yv6qLKt/tj1s7e48rnpScyPPWqHvz9ZuvGJj66YSWP749f0lZl//F+Pjgzwm4HWrU7ZUkmfT/WutdVV/HAbRv55Xtn+V3fyPTj2azh8Y44129Yyc0b7V3URZVn68Ymrls/887uBD34+5OIsHtnjM6+FC9/0HfRc3s6Ook01PKF651p1e6EJZn093R0srHFf7Xu99+6kZqqAE8UNPV6+YM+xxZ1UeWxdvbf9aV4+cO++V9QhtyKbnE+qgd/X/rctZexprH2ojP142dH+NX7fXztto3UBiunGd6SS/pWrfvD2/1X7ta6opa7b1jHs6/3cC49AeTqsdc01jq2qIsqz+evy+/sDt+s9fIHfXT2pSpqmmA5qQkGePD2KL/5MMn7p4cBeOJAnJpggPtvc7ZVu91KSvoicqeIvC8ix0XkmzM8XysiP8o//6qIRAue+7P84++LyGftC31mfq91f2RHjNHJKX74WjfvnT5Px/EkD94edWxRF1Wewp39gzPDjn3O3v25g//nrtWDv199dVs7ddUB9nbEOZee4LnXT3LPDeuINNR6HdqCzJtpRKQKeBT4HLAF+IqIbCnabDcwaIzZDPw18B/zr90C3AdcA9wJ/D/593OEVe523zb/lrttWdfI9stb+N4rCR77507qqgPcf2tljRSWm8Kd3Qnvnx7mNx/mDv41QT34+1VTuIY/vGkDPzlykkd/dZzRycpshlfKX9g24LgxptMYMwE8DdxdtM3dwJP5n58F7pDcOerdwNPGmHFjTBw4nn8/R1i17g/eHnXqI2yxe2eMU0NjPP/GSVcWdVHlsXb25988Sf/IuO3v79aKbqp8u3ZEmchk+e+/ibNzc4Sr1zZ6HdKClTIcXg8UNhjvAW6dbRtjTEZEhoCW/OMHi17rSBMcq9b9zmv9X+72yatWE4uEiSdTPOKD+wjU/HbtiPLUq138/v/VYftZZDyZ4ku3tNEU1oO/321evYLfu7KVlz/oY9fOqNfhLEopf70zXVUqrl+bbZtSXouIfB34OkB7++JGO8NjGXZujlTEFxEICP/7Pdfy7qnzbF7tzqIuqjybV6/g3995Nb89aX8Tti3rGvmTT262/X2VM/7s81ezZV0jn7hytdehLEopSb8HKLwqugEobiJjbdMjIkFgJTBQ4msxxjwGPAawdevWRRVEr2ms49H7b1rMSz2xY3OEHS7391fl+eNPXO51CMoHrl7byNV3Vt60jqWUOf1DwBUiEhORGnIXZvcVbbMPeCj/8xeBX5pck5l9wH356p4YcAXwmj2hK6WUWqh5R/r5OfpvAC8CVcBeY8wxEfkOcNgYsw/YA/ydiBwnN8K/L//aYyLyDPAOkAH+xBjjXiMTpZRSF5HZuj56ZevWrebw4cNeh6GUUhVFRF43xmydbzstClZKqWVEk75SSi0jmvSVUmoZ0aSvlFLLiCZ9pZRaRnxXvSMifcDsqxDPLwIkbQrHaZUUK1RWvJUUK1RWvJUUK1RWvOXEutEY0zrfRr5L+uUSkcOllC35QSXFCpUVbyXFCpUVbyXFCpUVrxux6vSOUkotI5r0lVJqGVmKSf8xrwNYgEqKFSor3kqKFSor3kqKFSorXsdjXXJz+koppWa3FEf6SimlZrFkkv58i7f7iYi0icivRORdETkmIv/K65jmIyJVIvKmiPyj17HMR0RWicizIvJe/v/j272OaTYi8q/zfwNvi8gPRaTO65gKicheETkrIm8XPNYsIr8QkQ/z/23yMkbLLLH+Vf7v4C0R+YmIrPIyxkIzxVvw3L8VESMiti+6sSSSfomLt/tJBvg3xpiPALcBf+LzeAH+FfCu10GU6P8E/skYczVwPT6NW0TWA/8LsNUYcy251uX3eRvVJZ4A7ix67JvAS8aYK4CX8r/7wRNcGusvgGuNMR8FPgD+zO2g5vAEl8aLiLQBnwa6nPjQJZH0KW3xdt8wxpwyxryR/3mYXFJyZO1gO4jIBuB/Av7W61jmIyKNwMfJrfGAMWbCGGP/Gof2CQL1+RXnQsywspyXjDH/TG6NjEJ3A0/mf34SuMfVoGYxU6zGmJ8bYzL5Xw+SW73PF2b5/xbgr4F/xwxLy9phqST9mRZv920SLSQiUeBG4FVvI5nT35D7I8x6HUgJNgF9wOP56ai/FZGw10HNxBhzEvjP5EZ0p4AhY8zPvY2qJGuMMacgN4ABKmWx2F3Az7wOYi4ichdw0hhz1KnPWCpJv6QF2P1GRBqA54D/1Rhz3ut4ZiIivw+cNca87nUsJQoCNwH/rzHmRiCFf6YfLpKfC78biAHrgLCIPOBtVEuTiHyL3LTqD7yOZTYiEgK+BXzbyc9ZKkm/pAXY/UREqskl/B8YY573Op457ADuEpEEuWmzfyEi3/c2pDn1AD3GGOvM6VlyBwE/+hQQN8b0GWMmgeeB7R7HVIozInIZQP6/Zz2OZ04i8hDw+8D9xt816peTGwAcze9vG4A3RGStnR+yVJJ+KYu3+4aICLk553eNMf/V63jmYoz5M2PMBmNMlNz/r780xvh2NGqMOQ10i8hV+YfuILdGsx91AbeJSCj/N3EHPr3oXGQf8FD+54eAf/AwljmJyJ3AvwfuMsakvY5nLsaY3xpjVhtjovn9rQe4Kf83bZslkfTzF2qsxdvfBZ4xxhzzNqo57QC+Rm7UfCT/7/NeB7WE/M/AD0TkLeAG4D94HM+M8mcjzwJvAL8ltz/66u5REfkh8ApwlYj0iMhu4C+BT4vIh+SqTP7Syxgts8T6fwMrgF/k97P/5mmQBWaJ1/nP9ffZjlJKKTstiZG+Ukqp0mjSV0qpZUSTvlJKLSOa9JVSahnRpK+UUsuIJn2llFpGNOkrpdQyoklfKaWWkf8fUzhRH4VwJSoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcaa14a18d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.03125 0.03125 0.03125 0.03125 0.28125 0.03125 0.03125 0.03125 0.03125\n",
      " 0.03125 0.03125 0.28125 0.03125 0.03125 0.0625 ]\n",
      "[0.03125 0.03125 0.03125 0.28125 0.03125 0.03125 0.03125 0.03125 0.03125\n",
      " 0.03125 0.03125 0.03125 0.28125 0.0625  0.03125]\n"
     ]
    },
    {
     "data": {
      "image/png": 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JpBKBWX+HSd8jVidmbf8gnxxJ4NzFMirV+rZ/FpEbutHJZpdJDWJusRyISYtM+h6R7eLpbLrZ28wJWuRV2S5NzLJMjTWKqdkF/w/xMOl7RFeTPidokcflCtvbPKVdkNbVZ9L3iFy+iOF4BEMxRztcrot75ZLXdauTzRKkXn0mfY/oRo++xfqwsIOHvKhcreHcxe50slkmmr36pwLQq8+k7xG5QqlrnQpDsQiGYxEO75Annck3Otm61a4JAOGQYM9oMJZYZtL3iG5W+gB79cm7rGHJ7WyT2EkmlQjErFwmfQ+oVOs4d7Hc1cpmMhnnmD55UmszoS5+HgBgKiDr6jPpe8CZQgmq3ZmYZdmTTHB4hzypm51sdplUAmcD0KvPpO8Bq5VN905nJ5NxnL1YxkqNE7TIW3L5Utc62ewyzV790z7v1WfS94BubADdLp2MQxWYWyx37WcS9cPsQnd79C1Wr77fl2Ng0vcAawPobo/p2382kVfkCt3t0bcEpVefSd8DsvkShmIRjMQHuvYzrfZPjuuT12TzJezpQaW/eziOgbAw6ZP7GrMPu3uQc9tE8qJedLJZwiHB3lH/t20y6XvAbJd79AFgJB7BYDQcmM2gyR/mFrvfyWaXCUDbpqOkLyI3isjzInJCRO7o8PibROQJEamKyLvaHquJyA+bX0e6FXiQ5LqwN247EUE6GUeu4O8DnPxldfOU7o/pA9YELX9/JjbseRKRMIC7AbwNwAyAoyJyRFWftT3tJQAfBPDxDj+iqKrXdCHWQFqp1TG3WO5JZZNmrz55TC862ewyqcZeE8VKrWtr9ZvGSaV/PYATqnpSVSsAHgBwk/0JqvoTVX0aAJu+u+zsYhmqvalsuBQDeU22B51sdlbb5ukF/47rO0n6ewGcst2ead7nVFxEjonIYyLyzk1FR6uVzWgvKv045hbLqHKCFnlENl/CjmgYw12emGWxNlM55eMhHif/ctLhPt3Ee+xT1VkRuQrAd0XkGVV98ZI3ELkNwG0AsG/fvk38aP/L9fB0djIZR62uOHex0rPKiaibcvkS0qMJiHRKS9sXhM1UnFT6MwCmbLczAGadvoGqzjb/PAngbwAc6vCce1R1WlWnx8fHnf7oQGjtjTvS/eEd6xfJLCdokUd0e7XZduNDMUTDIV+3bTpJ+kcBHBCRK0UkCuBmAI66cEQkJSKx5ve7ALwRwLPrv4rssvkSEgNhjCS6fzqb5mYq5DG5Lu+N2y4UEuxNJTAz799CaMOkr6pVALcDeATAcwAeVNXjInKXiBwGABG5TkRmALwbwBdE5Hjz5a8CcExEngLwPQCfbuv6oQ3kmpVNL05nuVcueUm1VsfcYm8rfcD/6+o7Kh9V9WEAD7fdd6ft+6NoDPu0v+4HAF69zRgDLZsv9my8PZkYQHwgxPV3yBPOXiyj3qNONrtMKoFvzxZ6+h5u4oxcwzUq/d4c5I0JWuzVJ2+wZo/3vtIfxPmlCpYr1Z6+j1uY9A1WqyvO9GhilmVyhL365A25HrYv21mrbZ72aQcPk77Bzl0so1bXnrZTppNxVvrkCb3sZLPze9smk77BZps7+PS00k/GcaZQQq2+makXRP2X62Enm91Uypqg5c+LuUz6Bsv1aC9Qu/RoAtW64vxF7qBFZssWetfJZrdrKIZoJMRKn/pvdXGp3p3OpkfYtkne0It9JToJhQQZH6+rz6RvsFyhhFgkhNRg93bMajfJXn3yiOxC79qX22XG/LuuPpO+wbI9nJhlSSe5Vy6Zz+pk29PjHn2Ln9fVZ9I3WK6HE7MsYzuiiIZDyBZY6ZO5+tHJZpdJJTC/VMFS2X+9+kz6Bptd6N3ELIuIYDIZR5bbJpLBer15Sjs/t20y6RuqXlecKfTnwlWam6mQ4XI93jylnTVBy48Xc5n0DXVuqYxqXftS2aSTcWS5Vy4ZrB+dbHZTrPSp31o9+j1cRtYymUzgTL6MOidokaFy+RKiPe5ks9s1FEUs4s919Zn0DWVVNntGe1/ZpJNxVGp1zC9Xev5eRFsx24dONjsR8W0HD5O+ofoxG9cy2Wrb5Lg+mSmXL/btIq4lkxr05VIMTPqGms0XEQ2HMDYY7fl7tbZNXPBfVUP+kO3hEuNrYaVPfZXLlzCRjCEU6v3pbKvSZ68+GaifnWx2mdQgFpZXsFha6ev79hqTvqGy+VLPl5C17NoRw0BYuBQDGen8UgUrtf50stlNjTXX1ffZGTCTvqH6tbgU0FhgaoKbqZCh+tnJZteaoOWzTdKZ9A2kqo1tEnu8Q5BdYzMVfx3c5A+tzVNcGNMH/DdBi0nfQPNLFVRq9dayx/0wmUyw0icjZfu0TWK7nTuiiA+EcMpnF3OZ9A2UbbVr9q+ysbZNVOUELTJLNl/qWyebXaNXf5CVPvVevxeXAhrjpeVqHReW/dWpQN6Xyxf71snWzo9tm0z6Bsrle783brt0azMVfx3g5H397GRrN5Xy32YqTPoGyuZLiIQEO4difXvPdHO5B47rk2lyLvToWzKpBPLFFRR81KvPpG+gXL6EiZE4wn08nU1z20QykKq2dpBzg9W2edpH1T6TvoHcOMh3DcUQDgkrfTLK/FIFlWrdxaTfOAM+Ne+fi7lM+gZy43Q2HBJMDMdY6ZNR3Ohks1vt1WelTz2iqphd6P+KgkBjDR5eyCWT5FzoZLMb2xHFYDTMpE+9s7C8gnK17kplk+YELTJMtuBu0l9dV5/DO9QjbvToWzhBi0yTyxf73snWLuOztk1HSV9EbhSR50XkhIjc0eHxN4nIEyJSFZF3tT12i4i80Py6pVuB+1Wu0N8NoO0mk3EUV2ooFKt9f2+iTrIudLK1y6QSvtpMZcOkLyJhAHcDeAeAgwDeKyIH2572EoAPAviztteOAfgUgNcBuB7Ap0Qktf2w/au1TaJLwzsAuEk6GaOfq82uJZNKYLFURb7oj159J5X+9QBOqOpJVa0AeADATfYnqOpPVPVpAPW2174dwKOqOq+qFwA8CuDGLsTtW7l8CeGQYHy4/6ezk+zVJ8O42aNvaS2x7JNq30nS3wvglO32TPM+J7bz2kDK5kvYPRxz5XQ2zb1yySCNiVnudLLZTbWSvj/OgJ0k/U7Zx+mVPkevFZHbROSYiBw7e/aswx/tT9l80bXT2fHhGEICZH22UxB5U764gtKKO51sdn7r1XeS9GcATNluZwDMOvz5jl6rqveo6rSqTo+Pjzv80f7k5unsQDiEcU7QIkO42clmNzo4gB3RcKCGd44COCAiV4pIFMDNAI44/PmPALhBRFLNC7g3NO+jDqwdsyZdWlEQaPbqc4N0MkBrm0SXk761rv4pn2ybuGHSV9UqgNvRSNbPAXhQVY+LyF0ichgAROQ6EZkB8G4AXxCR483XzgP4LTR+cRwFcFfzPuqgUKpiuVJztbKxevWJ3GZKpQ/AVxO0Ik6epKoPA3i47b47bd8fRWPoptNr7wVw7zZiDIzWlPM+bwtnN5mM4/svnHPt/Yks2XwR4ZBg97AZSf8ffjwPVYWIe3MGuoEzcg2SdWHzlHbpZBwXy1Us+mj9cPImNzvZ2k2NDWKxXPXFxEUmfYO4vaKg/b05xENuM2FilqW1xLIPhniY9A2SzZcgAux2YWKWhZupkClM6NG3ZHzUq8+kb5BcvojxoRgGwu79t6xO0PL+wU3eZe2Y5WYnm91qrz4rfeoiE6ac7x6OQ4SVPrlrsex+J5tdMjGAoViElT51Vy5fai165pZoJIRdQzEuxUCuMqGTzc5P6+oz6RvElAtX7NUnt80uuN/J1s4v6+oz6RtisbSCxXLViIN8coTbJpK7cgZ0srVrVPpFz28yxKRvCFOmnAOs9Ml9JnSytcukErhYrmJh2dtzWJj0DbE65dz9ymYy2dg04mLZ+xNRyJty+ZLrnWzt/NK2ac6/aMDlDFpnZM8o19Und2UL7neytfNL2yaTviGsSn9ixP0DfXKESZ/clXNxX4m1TI2x0qcuyhWK2DUUQzTi/n9Ja69cXswll2QNaF9ul0wMYDgeYaVP3WHCxCzL7pHGxTNW+uSGxoJ/ZnSytfND2yaTviGyC2b06ANAfCCMnTuimGXSJxdYS4CY8nmwy6QSnl90jUnfECYtLgU0PnBcf4fcYFInWzs/9Ooz6RtgqVxFoVQ1qrJhrz65xaQds9plUoNYrtRwwcO9+kz6BrD2pDXpIOdeueQW61qSdW3JJFM+aNtk0jdAzsDT2clkHAvLKyhWam6HQgGTzZewayiGWCTsdiiX8cMELSZ9A5h4OttaV5/VPvWZade37Pay0qduyDZXFDRhYpbFur5gxUbUL6asNttJMjGAkXgEp+a9+7lg0jdAtlDC2I4o4gPmnM6muVcuucSkOSudNHr1WenTNuTypdbSB6ZoLcXA4R3qo+VKFfniirGVPrDatulVTPoGMLGySUTDSA0OcCkG6iuTFh5cy9RYY1Zuve7NXn0mfQPk8kVjtoWzm0wmuBQD9ZWJnWztrt2XQnGlht/55nNuh7IlTPouK600JnqYeJBzghb1m4mdbO1+4dWTuOUNV+BPvv9j3P//fux2OJvGpO+y1o5Zho3pA9ZSDEz61D/WcKJJnWztRAR3/qurccPBCfyXv3oW3/pRzu2QNoVJ32WzefM2gLakR+I4v1RBaYUTtKg/snnzOtk6CYcEf3DzIVwzNYqPPPAkHv/pvNshOcak7zKT9sZtZ8V0hh081CcmdrKtJREN44sfmEY6Gce/+/IxnDx70e2QHGHSd5nJKwqyV5/6zcROtvXsHIrh/luvh4jgg/cdxbmLZbdD2pCjpC8iN4rI8yJyQkTu6PB4TET+vPn434vI/ub9+0WkKCI/bH59vrvhe18uX8Lo4AASUfNOZ9PcK5f6LFcwdzbuWvbv2oEv3TKNucUSPnT/USxXqm6HtK4Nk76IhAHcDeAdAA4CeK+IHGx72ocAXFDVlwP4HIDftT32oqpe0/z61S7F7RtZg09nrbhY6VM/lFZqmF+qYM+oeWe9Gzm0L4U/vPkQnjmdx4e/+iSqtbrbIa3JSaV/PYATqnpSVSsAHgBwU9tzbgLw5eb3DwF4i4hI98L0r1zB3MWldsQiGIlHuJkK9YXJnWxO3HD1JH7z8NX46+fm8Jt/edzYjVacJP29AE7Zbs807+v4HFWtAsgD2Nl87EoReVJE/lZE/vk24/WdxjaJ5lY26WSC2yZSX3ihR38jH3jDfvzKm6/Cnz72Ej7/tyfdDqejiIPndKrY23+FrfWcLIB9qnpeRH4OwP8WkatVtXDJi0VuA3AbAOzbt89BSP5QWqnh/FLF6IOcvfrUL7mCuXvjbsYn3v4zmF0o4Xe/9Y/YMxrHTde018juclLpzwCYst3OAJhd6zkiEgGQBDCvqmVVPQ8Aqvo4gBcBvKL9DVT1HlWdVtXp8fHxzf8tPGqu0LjSb/JBzlm51C9Zg9uXNyMUEnz23a/B664cw8e/9hR+8OI5t0O6hJOkfxTAARG5UkSiAG4GcKTtOUcA3NL8/l0AvquqKiLjzQvBEJGrABwAYOY5jwuyBk/MsqSTCZy7WEalau6FKfKHXL6EZGIAg1EnAxBmi0XCuOf909i/cwd+5X89judzi26H1LJh0m+O0d8O4BEAzwF4UFWPi8hdInK4+bQvAdgpIicAfBSA1db5JgBPi8hTaFzg/VVV9c7UtR5b3RvX5DF9TtCi/vBaj/5GkoMDuO/W65AYCOPW+/7BmM+Qoz59VX1YVV+hqi9T1d9u3nenqh5pfl9S1Xer6stV9XpVPdm8/+uqerWqvlZVr1XVv+zdX8V7vHA6O8ltE6lPcj5L+kBjw5X7br0O+eIKPnjfUSyWVtwOiTNy3ZRdKGI4HsFQzNzTWetDOMttE6nHsvmi0Z1sW3X1niT+6H0/h386s4h//5UnsOJyDz+Tvou8cDrbqvR5MZd6qFyt4dxFszvZtuPNrxjH7/zSq/H9F87hjq8/42oPv7klZgA0ppybXdkMxwcwFIuwg4d6ygudbNv1nukpzC4U8ft//QL2phL46Nsua2TsCyZ9F2XzJbxqcsTtMDbEXn3qNT9MzHLiI285gNmFIv7wOy9g72gc/+a6/s9LYtJ3SaVax7k9a0GiAAAGJklEQVSLZSO3SWyXTsaR5YVc6qHV9mWzz3y3S0Tw2//61cgVyvjP3/gRdo/E8fOv3N3XGDim75K5xRJUvVHZpJNxrr9DPWXyvhLdNhAO4Y9++Vq8cmIYv/aVJ/Cj0/m+vj+TvktWD3LzK5vJZAJzi2XXuw7Iv7L5kvGdbN00FIvgvluvQ2owilvvP4pT88t9e28mfZfMemgMM52MQxWYWzR/gwjypmze3NVme2ViJI77b70O5ZUabr3/KBaWK315XyZ9l1jDJV44nV1t2+QQD/VGLm9+J1svHJgYxj0fmMZL55dx2/98vC/7UfvmXGphuYJ3f/7v3A7DsXMXy9gRDWPYA6ezVgX263/2JHZ4IF7ynp+cX8IvHcq4HYYrXn/VTnz2Pa/Fh7/6JD72tafw328+hFCod9uR+OYTHAoJDkwMuR2GYwcmhnDtvhS8sNfMy8eH8P7XX4HzSxzeod54xcQw3nNdMJM+ABx+7R5kF4pYqtTQ65Qgpu3uMj09rceOHXM7DCIiTxGRx1V1eqPncUyfiChAmPSJiAKESZ+IKECY9ImIAoRJn4goQJj0iYgChEmfiChAmPSJiALEuMlZInIWwE+38SN2ATjXpXB6zUuxAt6K10uxAt6K10uxAt6KdzuxXqGq4xs9ybikv10icszJrDQTeClWwFvxeilWwFvxeilWwFvx9iNWDu8QEQUIkz4RUYD4Menf43YAm+ClWAFvxeulWAFvxeulWAFvxdvzWH03pk9ERGvzY6VPRERr8E3SF5EbReR5ETkhIne4Hc96RGRKRL4nIs+JyHER+YjbMW1ERMIi8qSI/JXbsWxEREZF5CER+cfmv/Eb3I5pLSLyH5vHwI9E5KsiYtT+mSJyr4jMiciPbPeNicijIvJC88+UmzFa1oj1M83j4GkR+YaIjLoZo12neG2PfVxEVER2dft9fZH0RSQM4G4A7wBwEMB7ReSgu1GtqwrgY6r6KgCvB/BrhscLAB8B8JzbQTj0BwC+pao/A+C1MDRuEdkL4MMAplX1ZwGEAdzsblSXuR/AjW333QHgO6p6AMB3mrdNcD8uj/VRAD+rqq8B8E8AfqPfQa3jflweL0RkCsDbALzUizf1RdIHcD2AE6p6UlUrAB4AcJPLMa1JVbOq+kTz+0U0ktJed6Nam4hkAPxLAF90O5aNiMgIgDcB+BIAqGpFVRfcjWpdEQAJEYkAGAQw63I8l1DV/wtgvu3umwB8ufn9lwG8s69BraFTrKr6bVWtNm8+BsCYPRnX+LcFgM8B+E8AenLB1S9Jfy+AU7bbMzA4idqJyH4AhwD8vbuRrOv30TgI624H4sBVAM4CuK85HPVFEdnhdlCdqOppAJ9Fo6LLAsir6rfdjcqRCVXNAo0CBsBul+Nx6t8C+KbbQaxHRA4DOK2qT/XqPfyS9DttJWx8W5KIDAH4OoD/oKoFt+PpRER+EcCcqj7udiwORQBcC+CPVfUQgCWYM/xwieZY+E0ArgSwB8AOEXmfu1H5k4h8Eo1h1a+4HctaRGQQwCcB3NnL9/FL0p8BMGW7nYFhp8ntRGQAjYT/FVX9C7fjWccbARwWkZ+gMWz2L0TkT90NaV0zAGZU1TpzegiNXwImeiuAH6vqWVVdAfAXAP6ZyzE5cUZE0gDQ/HPO5XjWJSK3APhFAL+sZveovwyNAuCp5uctA+AJEZns5pv4JekfBXBARK4UkSgaF8OOuBzTmkRE0Bhzfk5V/5vb8axHVX9DVTOquh+Nf9fvqqqx1aiq5gCcEpFXNu96C4BnXQxpPS8BeL2IDDaPibfA0IvObY4AuKX5/S0A/o+LsaxLRG4E8AkAh1V12e141qOqz6jqblXd3/y8zQC4tnlMd40vkn7zQs3tAB5B40PzoKoedzeqdb0RwPvRqJp/2Pz6BbeD8pFfB/AVEXkawDUA/qvL8XTUPBt5CMATAJ5B4/No1OxREfkqgL8D8EoRmRGRDwH4NIC3icgLaHSZfNrNGC1rxPo/AAwDeLT5Ofu8q0HarBFv79/X7LMdIiLqJl9U+kRE5AyTPhFRgDDpExEFCJM+EVGAMOkTEQUIkz4RUYAw6RMRBQiTPhFRgPx/qlF7Qii0vUIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcaa15b6b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.03125    0.03125    0.25       0.0625     0.0625     0.\n",
      " 0.         0.0625     0.0625     0.         0.         0.0625\n",
      " 0.03929248 0.30445752 0.03125   ]\n",
      "[0.03125    0.25       0.03125    0.0625     0.0625     0.\n",
      " 0.         0.0625     0.0625     0.         0.         0.03929248\n",
      " 0.0625     0.03125    0.30445752]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcaa14a1940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.203125   0.078125   0.078125   0.015625   0.03125    0.03125\n",
      " 0.03125    0.03125    0.03125    0.03125    0.01964624 0.01964624\n",
      " 0.00268083 0.09106917 0.30445752]\n"
     ]
    }
   ],
   "source": [
    "# Number of steps\n",
    "n_step=12\n",
    "for i in range(0,n_step):\n",
    "    if i > 0: # step = 0 doing nothing, only draw\n",
    "        if i%2 == 1 :\n",
    "            ch = Step1.dot(ch) # odd steps 1 3 5 ...\n",
    "        else:    \n",
    "            ch = Step2.dot(ch) # even steps 2 4 6 ...\n",
    "    ch2 = abs2(ch)  # calculate probabilities\n",
    "    print(ch2)\n",
    "    if i%2 == 0 : # plot for even steps 0 2 4 ...\n",
    "        plt.plot(ch2)\n",
    "        plt.show()\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
